^^Stress, strain, modulo di Young.

ref:  Storia.


Situazione: cilindro tirato o pressato assialmente


Ut tensio sic vis. L'allungamento causa la forza elastica.

ΔL       F=kΔL 


Strain, stress, modulo di Young.

F  =E  A






 =E  ΔL





strain, ε = ΔL/L, allungamento relativo.

ε =  ΔL


stress, sforzo, tensione

σ =  F


it: tensione interna (o sollecitazione interna o sforzo)

en: stress (force per unit area)

modulo di Young.

E =  σ


uniaxial stress
tensile or compressive stress in one direction and no stress in the other directions
is the diminutive of the Latin term modus which means measure



  1. Ut tensio sic vis.
  2. Stress, strain, modulo di Young. Storia.

  3. L'allungamento assottiglia l'elastico. Effetto Poisson.
  4. Tensione meccanica.
  5. Links inet

  6. wp/Young's_modulus
  7. wp/Elastic_modulus
  8. wp/Teoria_della_plasticità
  9. tecnologiameccanica/teoria-deformazione-plastica/dp_teoria-tensione-di-flusso




Strain stress  VS  stress strain

scelgo: l'ordine della formula, nel senso

stress in funzione di strain,  l'allungamento causa la forza.



  1. stress, strain
    c: originale
  2. Strain, stress, modulo di Young.
    c: 18_7_2020. Ho unito qui modulo di Young.







schey's equation

Y is the average flow stress of the material


flow stress    sforzo di flusso plastico



stres strain related by known constitutive equations.


constitutive equations
relate stress strain


The applied loads can cause



wp/Stres-strain_analysis | Analisi_delle_sollecitazioni

Stress-strain_curve (Yield curve (physics))



Uniaxial stress

A linear element of a structure is one that is essentially one dimensional and is often subject to axial loading only.

When a structural element is subjected to tension or compression its length will tend to elongate or shorten, and its cross-sectional area changes by an amount that depends on the Poisson's ratio of the material.

In engineering applications, structural members experience small deformations and the reduction in cross-sectional area is very small and can be neglected, i.e., the cross-sectional area is assumed constant during deformation.


For this case, the stress is called engineering stress or nominal stress and is calculated using the original cross section.

σe = P/Ao

P is the applied load

Ao is the original cross-sectional area.


In some other cases, e.g., elastomers and plastic materials, the change in cross-sectional area is significant. For the case of materials where the volume is conserved (i.e. Poisson's ratio = 0.5), if the true stress is desired, it must be calculated using the true cross-sectional area instead of the initial cross-sectional area, as:

σtrue = ( 1 + εe ) ( σe )

εe   nominal (engineering) strain

σe   nominal (engineering) stress.


The relationship between true strain and engineering strain is given by

εtrue = ln ⁡ ( 1 + εe )

In uniaxial tension, true stress is then greater than nominal stress. The converse holds in compression.